[EM] Associational Proportional Representation (APR) (Kristofer Munsterhjelm) 26

Kristofer Munsterhjelm km_elmet at t-online.de
Sat Nov 1 01:16:03 PDT 2014

On 10/31/2014 11:32 PM, Forest Simmons wrote:
> Kristofer wrote ...
> (huge skip)
>     This raises the question of where the optimal winners for weighted PR
>     should be placed. In particular, in an 1D spatial model (left-right
>     axis), it seems fair that the respective winners get a weight equal to
>     the proportion of voters that are closer to them than to anybody else.
>     But now we're much more free to place the winners anywhere on the axis
>     because the relative weight will sort itself out by the definition above
>     (unlike ordinary unweighted multiwinner elections).
>     The reasoning that we prefer moderates (but not too moderate ones) to
>     extremists to minimize tension could be codified like this: minimize the
>     sum of distances from voters to their representative.
> It seems to me that methods like APR that rely exclusively on ordinal
> information (rankings) cannot detect "distances."  For that we need some
> measure of intensity of preference like that provided by Approval and
> other Score based methods.

I'm not sure, actually. Consider Condorcet on a 1D spatial model. By 
Black's single-peakedness theorem, the candidate closest to the median 
is the CW, and the median is the single point that minimizes the sum of 
distances to every other point along the line. Yet Condorcet has no idea 
of distance beyond what the ranked votes tell it.

It might be the case that this can't be generalized to multiwinner 
methods. But it does at least show that it's not obviously impossible.

> I recently asked an APR supporter whom he thought should be seated in a
> 100 seat representative chamber if there were 100 candidates X1, X2,
> ...X100, each of whom was rated at 90 percent by every voter and also
> 100 candidates Y1, Y2, ... Y100, each of whom was rated 100 percent by
> exactly one percent of the population (and rated zero by the rest).
> I chose the extreme example to expose what I thought was the major
> shortcoming of any PR method that did not take into account intensity of
> preference.
> He replied that he thought that the Y's should be seated, since they
> would best represent the voters who voted for them.
> I was amazed: should we just throw away the wonderful opportunities for
> consensus as though it had no value?  Which would work better in Rwanda
> (think Hutu a Tutsi) or Iraq (think Shia and Sunni)?  It seems naive to
> me to think that fragmented PR can overcome the tyranny of the majority.

If there is a real trade-off between proportionality and majority 
quality (as by my graphs), and if there is no obvious or objective way 
of deciding what balance to choose, then the balance becomes a matter 
for the society in question.

At least on some level, that sounds sensible. Going more proportional 
means you have greater protection against a political oligopoly[1]. 
However, it can also increase factionalism. In a deeply divided society 
like civil-war era Rwanda, Iraq or Yugoslavia, the price you pay for 
going more proportional might not be worth it, while in a more moderate 
society, even politicians of wildly varying views can respect each other 
enough to find a consensus.

One'd imagine rated methods to be easier to tune than ranked ones, and 
to get the balance right more often. But on the rated side, voters might 
transform their votes without altering the rank. Normalization itself is 
a sort of linear transformation, and possibly the voters may also apply 
affine transformations. On the ranked side, if it is possible to design 
methods that generalize Black's result, they could determine the right 
"quantile candidates" even though there appears to be no obvious way for 
them to directly do so.

[1] It might seem that you could get more protection just by making the 
method small-party biased. However, I think that would give an incentive 
to perform clone management strategy like what is/was done in SNTV 
countries, and the big parties are better at coordinating strategy 
simply because of their size.

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